Optimizations for simulation algorithms:
One common optimization technique
is to group the Pauli strings into sets of mutually commutative strings and then apply simultaneous diagonalization [1]}, [2]}, [3]}, [4]}.
This technique, adopted by \(\rm t|ket\rangle \)  [5]}, [1]}, [2]}, [3]}, can simplify the circuit inside each set while the simultaneous diagonalization step introduces substantial overhead before and after the circuit of each set, limiting the overall optimization performance.
Some other works [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]} explore the simulation program optimization or synthesis but these works are mostly ad-hoc, limited to specific algorithms/architectures, and not easily generalizable to a broader range of programs and employed by a compiler infrastructure.
In Paulihedral, the Pauli IR's recursive, block-wise structure can support simulation kernels in all related algorithm, as far as we know.
And our optimization algorithms have been shown to be much more effective in the evaluation above.
